Question

If letters of the word PATANA are arranged in all possible ways as in the dictionary, then the word PATANA from the last is ?

Answer 1

`PATANA` consists of `4` letters. Occurance of `P` is `1`.
Occurance of `A` is `3`.
Occurance of `T` is `1`.
Occurance of `N` is `1`.
Now, number of words starting from `A = (5!)/((2!) = 60`
Number of words starting from `N = (5!)/(3!) = 20`
Number of words starting from `PAA = 3! = 6`
Number of words starting from `PAN = (3!)/(2!) = 3`
Number of words starting from `PATAA = 1`
So, total number of words that come before `PATANA = 60+20+6+3+1= 90`
Total number of words that can be formed by the given letters `= (6!)/(3!) = 120`
So, `PATANA` from last is ` = 120-90 = 30`